Abstract: We prove the following results. (1) If is the space of maps of the pseudo-arc into itself with the sup metric, then the subset of maps of the pseudo-arc into itself which are homeomorphisms onto their images is a dense in . (2) Every homeomorphism of the pseudo-arc onto itself is a product of -homeomorphisms. (3) There exists a nonidentity homeomorphism of the pseudo-arc with an infinite sequence of th roots. (4) Every map between chainable continua can be lifted to a homeomorphism of pseudo-arcs.